{"id":"https://openalex.org/W2940084603","doi":"https://doi.org/10.3390/sym11040523","title":"On Periodic Solutions of Delay Differential Equations with Impulses","display_name":"On Periodic Solutions of Delay Differential Equations with Impulses","publication_year":2019,"publication_date":"2019-04-11","ids":{"openalex":"https://openalex.org/W2940084603","doi":"https://doi.org/10.3390/sym11040523","mag":"2940084603"},"language":"en","primary_location":{"id":"doi:10.3390/sym11040523","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11040523","pdf_url":"https://www.mdpi.com/2073-8994/11/4/523/pdf?version=1554975754","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/11/4/523/pdf?version=1554975754","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015413492","display_name":"Mostafa Bachar","orcid":"https://orcid.org/0000-0002-0646-9067"},"institutions":[{"id":"https://openalex.org/I28022161","display_name":"King Saud University","ror":"https://ror.org/02f81g417","country_code":"SA","type":"education","lineage":["https://openalex.org/I28022161"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Mostafa Bachar","raw_affiliation_strings":["Department of Mathematics, College of Sciences, King Saud University, Riyadh 11451, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Sciences, King Saud University, Riyadh 11451, Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5015413492"],"corresponding_institution_ids":["https://openalex.org/I28022161"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.3292,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.77681568,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"11","issue":"4","first_page":"523","last_page":"523"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9793000221252441,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9793000221252441,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12021","display_name":"Social and Educational Sciences","score":0.9203000068664551,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9092000126838684,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/delay-differential-equation","display_name":"Delay differential equation","score":0.7294459939002991},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6740366220474243},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.6672336459159851},{"id":"https://openalex.org/keywords/c0-semigroup","display_name":"C0-semigroup","score":0.6308070421218872},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6027011871337891},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.581913411617279},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.5816909074783325},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5502399206161499},{"id":"https://openalex.org/keywords/distributed-parameter-system","display_name":"Distributed parameter system","score":0.4439102113246918},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.425258606672287},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.42137184739112854},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1963702142238617},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1357910931110382}],"concepts":[{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.7294459939002991},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6740366220474243},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.6672336459159851},{"id":"https://openalex.org/C19496378","wikidata":"https://www.wikidata.org/wiki/Q846542","display_name":"C0-semigroup","level":3,"score":0.6308070421218872},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6027011871337891},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.581913411617279},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.5816909074783325},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5502399206161499},{"id":"https://openalex.org/C112714845","wikidata":"https://www.wikidata.org/wiki/Q1482001","display_name":"Distributed parameter system","level":3,"score":0.4439102113246918},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.425258606672287},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.42137184739112854},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1963702142238617},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1357910931110382},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym11040523","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11040523","pdf_url":"https://www.mdpi.com/2073-8994/11/4/523/pdf?version=1554975754","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:85c7aedd897d4d43902465a3edab6d75","is_oa":true,"landing_page_url":"https://doaj.org/article/85c7aedd897d4d43902465a3edab6d75","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 11, Iss 4, p 523 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym11040523","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11040523","pdf_url":"https://www.mdpi.com/2073-8994/11/4/523/pdf?version=1554975754","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3722308287","display_name":null,"funder_award_id":"RG-1435-079","funder_id":"https://openalex.org/F4320321145","funder_display_name":"King Saud University"}],"funders":[{"id":"https://openalex.org/F4320321145","display_name":"King Saud University","ror":"https://ror.org/02f81g417"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2940084603.pdf","grobid_xml":"https://content.openalex.org/works/W2940084603.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W628962280","https://openalex.org/W1555674425","https://openalex.org/W1855169650","https://openalex.org/W1984935035","https://openalex.org/W2034352676","https://openalex.org/W2048544799","https://openalex.org/W2079871064","https://openalex.org/W2122792804","https://openalex.org/W2131706225","https://openalex.org/W2147270944","https://openalex.org/W2166026801","https://openalex.org/W2209983182","https://openalex.org/W2278091332","https://openalex.org/W2520740059","https://openalex.org/W2619753260","https://openalex.org/W2677548544","https://openalex.org/W2793145660","https://openalex.org/W2801934699","https://openalex.org/W4246201775","https://openalex.org/W6694851441","https://openalex.org/W6738521814"],"related_works":["https://openalex.org/W2846516035","https://openalex.org/W4249977926","https://openalex.org/W2585118952","https://openalex.org/W2012141574","https://openalex.org/W1606221119","https://openalex.org/W2354765335","https://openalex.org/W3123504591","https://openalex.org/W2369544116","https://openalex.org/W1691643469","https://openalex.org/W2985828462"],"abstract_inverted_index":{"The":[0,36],"purpose":[1],"of":[2,38,42],"this":[3],"paper":[4],"is":[5,47],"to":[6],"study":[7],"the":[8,18,39,51],"nonlinear":[9],"distributed":[10],"delay":[11,44],"differential":[12,45],"equations":[13,46],"with":[14],"impulses":[15],"effects":[16],"in":[17,56],"vectorial":[19],"regulated":[20,57],"Banach":[21],"spaces":[22],"R":[23,32,59,68],"(":[24,60],"[":[25,61],"\u2212":[26,62],"r":[27,63],",":[28,31,64,67],"0":[29,65],"]":[30,66],"n":[33,69],")":[34,70],".":[35,71],"existence":[37],"periodic":[40],"solution":[41],"impulsive":[43],"obtained":[48],"by":[49],"using":[50],"Sch\u00e4ffer":[52],"fixed":[53],"point":[54],"theorem":[55],"space":[58]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":2}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
